%I #9 Dec 24 2017 09:27:17

%S 9,6,6,2,7,3,9,6,1,5,7,6,7,1,2,9,5,7,2,0,9,3,8,8,6,4,9,0,0,9,2,1,2,4,

%T 8,1,6,3,4,4,4,6,9,2,6,1,3,1,5,3,9,1,4,2,4,2,6,3,4,9,7,1,5,7,5,1,3,2,

%U 2,7,8,5,0,7,6,4,4,7,6,0,1,3,2,0,4,7,0,9,0,0,1,3,2,9,1,2,4,2,1,1

%N Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(sqrt(2),sqrt(3),sqrt(5)).

%C See A195284 for definitions and a general discussion.

%H G. C. Greubel, <a href="/A195365/b195365.txt">Table of n, a(n) for n = 0..10000</a>

%e (A)=0.96627396157671295720938864900921248163444...

%t a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];

%t f = 2 a*b/(a + b + c);

%t x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]

%t x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]

%t x3 = f*Sqrt[2]

%t N[x1, 100]

%t RealDigits[%] (* (A) A195365 *)

%t N[x2, 100]

%t RealDigits[%] (* (B) A195366 *)

%t N[x3, 100]

%t RealDigits[%] (* (C) A195367 *)

%t N[(x1 + x2 + x3)/(a + b + c), 100]

%t RealDigits[%] (* Philo(ABC,I) A195368 *)

%Y Cf. A195284, A195366, A195367, A195368.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 16 2011